Chapter 6
6 –10C Baseboard heaters are basically basically electric resistance heaters and are frequently used in space space heating. A home owner claims that her 5-year-old baseboard heaters have a conversion efficiency of 100 percent. Is this claim in violation of any thermodynamic laws? Explain. 6 –15 A steam power plant receives heat from a furnace at at a rate of 280 GJ/h. Heat losses to the surrounding air from the steam as it passes through the pipes and other components are estimated to be about 8 GJ/h. If the waste heat is transferred to the cooling water at a rate of 145 GJ/h, determine (a) net power output and (b) the thermal efficiency of this power plant. plant. Answers: (a) 35.3 MW, (b) 45.4 percent 6 –26 A coal-burning steam power power plant produces produces a net power of 300 MW with an overall overall thermal –fuel ratio in the furnace is calculated to be 12 kg efficiency of 32 percent. The actual actual gravimetric air – air/kg fuel. The heating value of the coal is 28,000 kJ/kg. Determine (a) the amount of coal consumed during a 24-hour period and (b) the rate of air flowing through the furnace. Answers: (a) 2.89 x10 6 kg, (b) 402 kg/s
Refrigerators and Heat Pumps
6 –39 Determine the COP of a heat pump that supplies energy to a house at a rate of 8000 kJ/h for each kW of electric power it draws. Also, determine the rate of energy absorption from the outdoor air. Answers: 2.22, 4400 kJ/h 6 –42 An air conditioner conditioner removes removes heat heat steadily from from a house at a rate of 750 kJ/min kJ/min while drawing electric power at a rate of 6 kW. Determine (a) the COP of this air conditioner and (b) the rate of heat transfer to the outside air. Answers: (a) 2.08, (b) 1110 kJ/min 6 –43 A food department department is kept at 212degC 212degC by a refrigerator refrigerator in an environment at 30degC. The total heat gain to the food department is estimated to be 3300 kJ/h and the heat rejection in the condenser is 4800 kJ/h. Determine the power input to the compressor, in kW and the COP of the refrigerator. Answer:
6 –44 A household refrigerator that has a power input of 450 W and a COP of 1.5 is to cool 5 large large watermelons, 10 kg each, to 8degC. If the watermelons are initially at 28degC, determine how long it will take for the refrigerator to cool them. The watermelons can be treated as water whose specific heat is 4.2 kJ/kg·degC. Is your answer realistic or optimistic? Explain. Answer: 104 min
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6 –49 A heat pump is used to maintain a house at a constant temperature of 23degC. The house is losing heat to the outside air through the walls and the windows at a rate of 85,000 kJ/h while the energy generated within the house from people, lights, and appliances amounts to 4000 kJ/h. For a COP of 3.2, determine the required power input to the heat pump. Answer: 7.03 kW
6 –54 Consider a building whose annual air-conditioning load is estimated to be 40,000 kWh in an area where the unit cost of electricity is $0.10/kWh. Two air conditioners are considered for the building. Air conditioner A has a seasonal average COP of 2.3 and costs $5500 to purchase and install. Air conditioner B has a seasonal average COP of 3.6 and costs $7000 to purchase and install. All else being equal, determine which air conditioner is a better buy.
6 –55 Refrigerant-134a enters the condenser of a residential heat pump at 800 kPa and 35degC at a rate of 0.018 kg/s and leaves at 800 kPa as a saturated liquid. If the compressor consumes 1.2 kW of power, determine (a) the COP of the heat pump and (b) the rate of heat absorption from the outside air.
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Carnot Heat Engines
6 –77 A Carnot heat engine operates between a source at 1000 K and a sink at 300 K. If the heat engine is supplied with heat at a rate of 800 kJ/min, determine (a) the thermal efficiency and (b) the power output of this heat engine. Answers: (a) 70 percent, (b) 9.33 kW 6 –82 In tropical climates, the water near the surface of the ocean remains warm throughout the year as a result of solar energy absorption. In the deeper parts of the ocean, however, the water remains at a relatively low temperature since the sun’s rays cannot penetrate very far. It is propose d to take advantage of this temperature difference and construct a power plant that will absorb heat from the warm water near the surface and reject the waste heat to the cold water a few hundred meters below. Determine the maximum thermal efficiency of such a plant if the water temperatures at the two respective locations are 24 and 3degC.
Carnot Refrigerators and Heat Pumps
6 –91 A Carnot refrigerator operates in a room in which the temperature is 22degC and consumes 2 kW of power when operating. If the food compartment of the refrigerator is to be maintained at 3degC, determine the rate of heat removal from the food compartment. 6 –92 An air-conditioning system operating on the reversed Carnot cycle is required to transfer heat from a house at a rate of 750 kJ/min to maintain its temperature at 24degC. If the outdoor air temperature is 35degC, determine the power required to operate this air-conditioning system. Answer: 0.46 kW 6 –94 A heat pump operates on a Carnot heat pump cycle with a COP of 8.7. It keeps a space at 24degC by consuming 2.15 kW of power. Determine the temperature of the reservoir from which the heat is absorbed and the heating load provided by the heat pump. Answers: 263 K, 18.7 kW 6 –101 A commercial refrigerator with refrigerant-134a as the working fluid is used to keep the refrigerated space at 235degC by rejecting waste heat to cooling water that enters the condenser at 18degC at a rate of 0.25 kg/s and leaves at 26degC. The refrigerant enters the condenser at 1.2 MPa and 50degC and leaves at the same pressure sub- cooled by 5degC. If the compressor consumes 3.3kW of power, determine (a) the mass flow rate of the refrigerant, (b) the refrigeration load, (c) the COP, and (d) the minimum power input to the compressor for the same refrigeration load.
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6 –137 A heat pump supplies heat energy to a house at the rate of 140,000 kJ/h when the house is maintained at 25degC. Over a period of one month, the heat pump operates for 100 hours to transfer energy from a heat source outside the house to inside the house. Consider a heat pump receiving heat from two different outside energy sources. In one application the heat pump receives heat from the outside air at 0degC. In a second application the heat pump receives heat from a lake having a water temperature of 10degC. If electricity costs $0.105/kWh, determine the maximum money saved by using the lake water rather than the outside air as the outside energy source. 6 –138 The cargo space of a refrigerated truck whose inner dimensions are 12 m 3 2.3 m 3 3.5 m is to be precooled from 25degC to an average temperature of 5degC. The construction of the truck is such that a transmission heat gain occurs at a rate of 120 W/degC. If the ambient temperature is 25degC, determine how long it will take for a system with a refrigeration capacity of 11 kW to precool this truck. 6 –139 The maximum flow rate of a standard shower head is about 3.5 gpm (13.3 L/min) and can be reduced to 2.75 gpm (10.5 L/min) by switching to a low-flow shower head that is equipped with flow controllers. Consider a family of four, with each person taking a 6-minute shower every morning. City water at 15degC is heated to 55degC in an oil water heater whose efficiency is 65 percent and then tempered to 42degC by cold water at the T-elbow of the shower before being routed to the shower head. The price of heating oil is $2.80/gal and its heating value is 146,300 kJ/gal. Assuming a constant specific heat of 4.18 kJ/kg ∙ degC for water, determine the amount of oil and money saved per year by replacing the standard shower heads by the low-flow ones. 6 –141 A refrigeration system is to cool bread loaves with an average mass of 350 g from 30 to 210degC at a rate of 1200 loaves per hour by refrigerated air at 230degC. Taking the average specific and latent heats of bread to be 2.93 kJ/kg·degC and 109.3 kJ/kg, respectively, determine (a) the rate of heat removal from the breads, in kJ/h; (b) the required volume flow rate of air, in m3/h, if the temperature rise of air is not to exceed 8degC; and (c) the size of the compressor of the refrigeration system, in kW, for a COP of 1.2 for the refrigeration system. 6 –147 The kitchen, bath, and other ventilation fans in a house should be used sparingly since these fans can discharge a houseful of warmed or cooled air in just one hour. Consider a 200m2 house whose ceiling height is 2.8 m. The house is heated by a 96 percent efficient gas heater and is maintained at 22degC and 92 kPa. If the unit cost of natural gas is $1.20/therm (1 therm 5 105,500 kJ), determine the cost of energy “vented out” by the fans in 1 h. Assume the average outdoor temperature during the heating season to be 5degC. 6 –151 A heat pump receives heat from a lake that has an average winter time temperature of 6degC and supplies heat into a house having an average temperature of 23degC. (a) If the house loses heat to the atmosphere at the rate of 52,000 kJ/h, determine the minimum power supplied to the heat pump, in kW. (b) A heat exchanger is used to transfer the energy from the lake water to the heat pump. If the lake water temperature decreases by 5degC as it flows through the lake water-to-heat pump heat exchanger, determine the minimum mass flow rate of lake water, in kg/s. Neglect the effect of the lake water pump.
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